Steven N. Karp Department of Mathematics University of Notre Dame 255 Hurley Hall Notre Dame, IN 46556 Office: 108 Hayes-Healy Center Email: skarp2@nd.edu Office phone: 574-631-8706

I am an Assistant Professor of Mathematics at the University of Notre Dame. My research area is algebraic combinatorics.

CV

Publications and preprints

Also see arXiv, Google Scholar, MathSciNet, ORCID, and zbMATH.

• (with Evgeny Mukhin and Vitaly Tarasov) Positivity and universal Plücker coordinates for spaces of quasi-exponentials. arXiv:2405.20229
• (with Kevin Purbhoo) Universal Plücker coordinates for the Wronski map and positivity in real Schubert calculus. arXiv:2309.04645
• (with Anthony M. Bloch) Symmetric Toda, gradient flows, and tridiagonalization. Phys. D 450 (2023), Paper No. 133766, 10 pp., in honor of Hermann Flaschka. arXiv:2304.10697
• (with Hugh Thomas) q-Whittaker functions, finite fields, and Jordan forms. arXiv:2207.12590
• (with Anthony M. Bloch) On two notions of total positivity for partial flag varieties. Adv. Math. 414 (2023), Paper No. 108855, 24 pp. arXiv:2206.05806
• Wronskians, total positivity, and real Schubert calculus. Selecta Math. (N.S.) 30 (2024), no. 1, Paper No. 1, 28 pp. arXiv:2110.02301
• (with Anthony M. Bloch) Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties. Comm. Math. Phys. 398 (2023), no. 3, 1213–1289. arXiv:2109.04558
• (with John Machacek) Shelling the m=1 amplituhedron. Comb. Theory 3 (2023), no. 1, Paper No. 6, 22 pp. arXiv:2104.02786
• (with Pavel Galashin and Thomas Lam) Regularity theorem for totally nonnegative flag varieties. J. Amer. Math. Soc. 35 (2022), no. 2, 513–579. arXiv:1904.00527
• Moment curves and cyclic symmetry for positive Grassmannians. Bull. Lond. Math. Soc. 51 (2019), no. 5, 900–916. arXiv:1805.06004
• (with Pavel Galashin and Thomas Lam) The totally nonnegative part of G/P is a ball. Adv. Math. 351 (2019), 614–620. arXiv:1801.08953
• (with Lauren K. Williams and Yan X Zhang) Decompositions of amplituhedra. Appendix written with Hugh Thomas. Ann. Inst. Henri Poincaré D 7 (2020), no. 3, 303–363. arXiv:1708.09525
• (with Pavel Galashin and Thomas Lam) The totally nonnegative Grassmannian is a ball. Adv. Math. 397 (2022), Paper No. 108123, 23 pp. arXiv:1707.02010
• (with Lauren K. Williams) The m=1 amplituhedron and cyclic hyperplane arrangements. Int. Math. Res. Not. IMRN (2019), no. 5, 1401–1462. arXiv:1608.08288
• Sign variation, the Grassmannian, and total positivity. J. Combin. Theory Ser. A 145 (2017), 308–339. arXiv:1503.05622
• (with R. P. Anstee) Forbidden Configurations: Exact bounds determined by critical substructures. Electronic J. Combin. 17 (2010), no. 1, Research Paper 50, 27 pp.

Teaching (University of Notre Dame)

• Fall 2024: Math 30210 (Introduction to operations research); Math 30530 (Introduction to probability).
  
• Spring 2024: Math 60610 (Basic discrete mathematics).
  
• Fall 2023: Math 20550 (Calculus III), sections 5 and 6.
  
• Spring 2023: Math 20580 (Introduction to linear algebra and differential equations), section 3; Math 40210 (Basic combinatorics).
  
• Fall 2022: Math 30530 (Introduction to probability).
  

Teaching (University of Michigan)

• Winter 2019: Math 217 (Linear algebra), section 10.
  
• Fall 2018: Math 217 (Linear algebra), sections 1 and 4.
  
• Winter 2018: Math 566 (Algebraic combinatorics).
• Fall 2017: Math 115 (Calculus I), sections 18 and 38.
  

Talk slides

• University of California, Los Angeles, October 2024: Positivity in real Schubert calculus
  
• FPSAC 2024: Positivity in real Schubert calculus
  
• University of Illinois Urbana–Champaign, April 2024: Positivity in real Schubert calculus
  
• Richard P. Stanley seminar in combinatorics, March 2024: Positivity in real Schubert calculus
  
• University of Texas at Austin, February 2024: Positivity in real Schubert calculus
  
• Purdue University, February 2024: Gradient flows on totally nonnegative flag varieties
  
• Indiana University–Purdue University Indianapolis, January 2024: Positivity in real Schubert calculus
  
• University of Minnesota, January 2024: Positivity in real Schubert calculus
  
• Hamiltonian systems seminar, November 2023: Gradient flows on totally nonnegative flag varieties
  
• Texas A&M University, September 2023: Positivity in real Schubert calculus
  
• Washington University, April 2023: Gradient flows on totally nonnegative flag varieties
  
• University of Kentucky, March 2023: q-Whittaker functions, finite fields, and Jordan forms
  
• University of Michigan, September 2022: q-Whittaker functions, finite fields, and Jordan forms
  
• University of Notre Dame, September 2022: Wronskians, total positivity, and real Schubert calculus
  
• University of Washington, April 2022: q-Whittaker functions, finite fields, and Jordan forms
  
• MFO mini-workshop, December 2021: Gradient flows on totally nonnegative flag varieties
  
• CMS winter meeting, December 2021: Wronskians, total positivity, and real Schubert calculus
  
• Center of Mathematical Sciences and Applications, November 2021: Gradient flows on totally nonnegative flag varieties
  
• North Carolina State University, October 2021: Wronskians, total positivity, and real Schubert calculus
  
• Washington University, September 2021: Wronskians, total positivity, and real Schubert calculus
  
• University of Waterloo, May 2021: q-Whittaker functions, finite fields, and Jordan forms
  
• Amplituhedron day, April 2021: Introduction to the amplituhedron
  
• CAAC 2021: q-Whittaker functions, finite fields, and Jordan forms
  
• AMS special session, October 2020: Regularity theorem for totally nonnegative flag varieties
  
• FPSAC 2020: Regularity theorem for totally nonnegative flag varieties
  
• ALGECOM-XIX: Topology of totally positive spaces
  
• LaCIM, Université du Québec à Montréal, January 2020: Topology of totally positive spaces
  
• The Ohio State University, March 2019: Combinatorics of the amplituhedron
  
• Massachusetts Institute of Technology and Microsoft Research, November 2018: Topology of positive spaces
  
• University of Massachusetts Amherst, November 2018: Combinatorics of the amplituhedron
  
• AMS special session, October 2018: Geometry of the amplituhedron
  
• FPSAC 2018: The totally nonnegative Grassmannian is a ball
  
• CAMP 2018: Geometry of the amplituhedron
  
• University of Michigan, October 2017: Topology of positive spaces
  
• University of Minnesota, September 2017: Cyclic symmetry in the Grassmannian
  
• FPSAC 2017: The m=1 amplituhedron and cyclic hyperplane arrangements
  
• Texas State University, April 2016: Sign variation, the Grassmannian, and total positivity
  
• University of Michigan, February 2016: Sign variation, the Grassmannian, and total positivity
  
• FPSAC 2015: Sign variation, the Grassmannian, and total positivity